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Early Voltage in MOSFETs. Due to channel length modulation:. Saturation Voltage. V pinchoff = V DS,sat = V GS – V TH Separates resistive from saturation region The drain current is given by Solving for V DS,sat : Good to solve for quiescent voltage-current.

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early voltage in mosfets
Early Voltage in MOSFETs
  • Due to channel length modulation:

Brad Noble

Chapter 3 Slides

saturation voltage
Saturation Voltage
  • Vpinchoff = VDS,sat = VGS – VTH
    • Separates resistive from saturation region
  • The drain current is given by
  • Solving for VDS,sat:
  • Good to solve for quiescent voltage-current.

Brad Noble

Chapter 3 Slides

ex find v ds sat for an nfet
Ex: Find VDS,sat for an NFET

Brad Noble

Chapter 3 Slides

variations in v th across channel

Cox

Gate oxidecapacitance

inversionlayer

Depletion cap,function of x

Cdep

Variations in VTHAcross Channel
  • We assume VTH is constant across channel

THIS IS NOT TRUE!

  • Depletion region is thick at S and thin at D.

Brad Noble

Chapter 3 Slides

notes on pfets
Notes on PFETs
  • PFETs typically have a shape factor 3 or 4 times larger than NFETs
  • Body effect can be eliminated in PFETs by tying the n-well to VDD
    • Need 6m spacing between n-wells to isolate.
    • Dr. Engel always does this on input devices, not always elsewhere.

Brad Noble

Chapter 3 Slides

weak inversion
Weak Inversion
  • What really happens if VGS < VTN?
  • In digital design, IDS = 0.
  • We call it “weak inversion” or W.I.
  • IDS is primarily due to Idrift in strong inversion and Idiffusion in weak inversion.

Brad Noble

Chapter 3 Slides

modes of inversion
Modes of Inversion
  • IDS = Idrift + Idiffusion
  • If VGS > VTN the channel has been inverted.
  • To be more precise, we can say the channel has been “strongly inverted” (S.I.) due to an abundance of carriers in the channel.
  • Inversion is independent of whether the FET is in the linear or saturation region.

Brad Noble

Chapter 3 Slides

weak inversion i diffusion
Weak Inversion Idiffusion
  • Drain is more reverse biased than source:
  • To find Idiff, compute gradient
  • Because no carriers are lost as they travel from S to D, current is the same for all x and gradient is not a function of x.
  • Note: This is not really true due to recombination, but its close!

Brad Noble

Chapter 3 Slides

w i surface potential
W.I. Surface Potential

Brad Noble

Chapter 3 Slides

deriving weak inversion i ds
Deriving Weak Inversion IDS

Brad Noble

Chapter 3 Slides

w i fet as exp law dev
W.I. FET As Exp. Law Dev.
  • S must be big for device to be useful.
  • If VDS = 100mV, can be neglected.
  • For W.I. vDS,Sat 100mV
  • Looks like a BJT

Brad Noble

Chapter 3 Slides

inversion coefficient
Inversion Coefficient
  • Let
  • Shape factor as a function of  :

Lets you chose shape to match inversion mode.

Brad Noble

Chapter 3 Slides

ex using inversion coeff
Ex. Using Inversion Coeff.

Brad Noble

Chapter 3 Slides

small signal analysis
Small Signal Analysis

Brad Noble

Chapter 3 Slides

ex quiescent point
Ex: Quiescent Point

Question: How many digits are significant?

Brad Noble

Chapter 3 Slides

small signal model limits
Small Signal Model Limits
  • Suppose the previous circuit is the input device of an amplifier.
  • Small-signal model holds as long as the deviations are small

Brad Noble

Chapter 3 Slides

taylor series expansion
Taylor Series Expansion
  • Taking a Taylor expansion of one variable:

Brad Noble

Chapter 3 Slides

small signal model params
Small Signal Model Params

Brad Noble

Chapter 3 Slides

example small signal analysis
Example: Small Signal Analysis

Brad Noble

Chapter 3 Slides

small signal low freq model
Small Signal Low-Freq Model

Brad Noble

Chapter 3 Slides

ex find g m and r o
Ex: Find gm and rO

Brad Noble

Chapter 3 Slides

transconductance w i m i
Transconductance: W.I. & M.I.
  • What is gm for a weakly inverted FET?
  • What is gm for a moderately inverted FET?

Not in textbooks!

Brad Noble

Chapter 3 Slides

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